So far we have only talked about the primary descendants or null states under the global conformal group \(SL(2,\mathbb {C})\) . But what about the Virasoro algebra? In fact in \(D=3+1\)  it has been conjectured that the \(SL(2,\mathbb {C})\)  conformal group gets enhanced to the full Virasoro algebra or the algebra of super-rotations [1]}, [2]}. Decoupling of Virasoro null-states has a far richer story. So it is natural to wonder what happens in \(D=3+1\)  if instead of \(SL(2,\mathbb {C})\)  we let the Virasoro null-states to decouple. May be this is more natural. In fact we have seen that in \(D=3+1\) , Lorentz invariance does not require decoupling of null-state, but, the theories in which null-states decouple are certainly more solvable or simpler. We know from our experience with 2-D CFTs that decoupling of Virasoro null-states can even make a theory exactly solvable. So the existence of Virasoro or super-rotation in \(D=3+1\)  perhaps points to a far more solvable \(3+1\)  dimensional theory. So it will be interesting to explore the role Virasoro null states in \(D=3+1\) . This will of course require an understanding of the central term.
